Abstract: In a recent paper, R. A. R. Monzo characterized semilattices of rectangular bands and groups of exponent 2. However, his characterization does not seem to point directly to the properties of rectangular bands and groups of exponent 2 (namely, idempotency and commutativity). My work consisted in proving a natural characterization of this type of semillatice. This research was carried out under the supervision of Professor Michael Kinyon from Denver University.